By way of example, WO Publication No. 2010/022699 A1, also published as U.S. Pat. No. 8,785,951 B2, describes an optoelectronic component which emits mixed-colored radiation. For this purpose the component comprises a radiation-emitting semiconductor chip and a conversion element spanning the semiconductor chip. Such a conversion element, which is arranged in a manner remote from the semiconductor chip and has a three-dimensional structure, is designated as a “remote phosphor” element. Although such a component has a relatively high conversion efficiency on account of the three-dimensional structure, it has significantly larger dimensions than the semiconductor chip.